What Sal does at 9:04 is one of the things that make it so easy to learn from him. He clarifies why he is using sin(1) even though it would be obvious to a lot of people. Teachers generally assume that the students know the reasoning behind every single step in their calculations, which isn't always the case. Thanks a lot, Sal.
I seriously can't thank you enough. My math professor's ineptitude is rivaled only by your competence in explaining the same material. I went into that lecture less confused than I was leaving, whereas this video provides a crystal-clear explanation. Who knows? If there were someone like you for every major subject, TH-cam could serve as a viable replacement for college. Cheers!
I had the assigned notes on this for my calculus course, but I couldn't understand. I read it over, and over, and gave a week space in between so I can have a fresh look at the concept of Taylors Polynomial. I heard your site, checked out on how you were teaching the concept... and wow... best 18 minutes of my life spent ACADEMICALLY! Thank you.
Don't be sorry Sal, you deserve all the walnuts you could ever want for explaining this so well! I wish more people would take the time to explain the reasons behind maths functions, it makes it so much easier to see why and what's happening.
I did the former. Each added term contributes to the approximation and doesn't replace it. So the approximation with 100 terms would be much better than the approximation with 2 terms.
Had Numerical Analysis class for the first time at the start of semester today. He made me feel like a complete moron because he sped through Taylor Polynomials in class as if it was the simplest thing in the world to just pick up. This taught me more in 18 minutes than my teacher could in an hour and fifteen. Seriously, why can't more professors be this good?
This is just fantastic! At my university I was only taught how to use the Taylor Series like it's some magical formula you just have to remember, but don't need to understand. In less than twenty minutes you managed to explain what exactly it is and how it is used. Thanks a lot!
To answer a question that's popped up a couple times below: Doing a Taylor expansion for certain functions makes evaluating them around a certain point easier than evaluating the actual function. For example, doing this for sin(x) or tan(x) for SMALL values of x, the later terms of the expansion are so small that you can approximate sin(x) [or tan(x)] to equal x. Cool, right? Here's what I mean: en.wikipedia.org/wiki/Small-angle_approximation
this is amazing since, after seeing so many classes, and knowing that males are visual, only this guy decides to make taylor visual. Thx for putting "visual males" and "math" together.
I reviewed these videos again, and understand it now. Indeed, even the approximation at n=0, that is, where it's just a straight line or constant, is equal to the function at point c. Making the approximations better by adding more terms gives you better approximations at points "near" c and, with even better approximations with more terms, further away from point c. THANKS SAL!
Holy shit O.O I've not gone to a single lesson we have so far because the teacher is so bad, and i think i'm about to pass the whole course just by your videos.
@someonetoogoodforyou The nth derivative is not equal to the function. It's equal to the function at c. As the nth derivative approaches infinity, not only does p(x) equal f(x) at c, but some of the terms near c of p(x) are close to the terms of f(x) near c. The more derivatives, the closer the values near c of p(x) are to the values near c of f(x) and the farther from c you can approximate. Theoretically, taking infinite derivatives will make the two functions equal for all x.
i see a bit of remainder therorem here...where polynomials is evaluated at c and its easy to understand only if you know FIRST PRINCIPLE OF DIFFERENTIAL AND TRIGONOMETRY WELL. THE reason I say first principle is you need to know why derivative of sin cos tan cosec sec and all...
Just wanted to say, I bet the reason everybody is on this video is because their professors make it SO difficult to understand. This makes it look SO easy so thanks again Sal =)
Nicely stitched video. Taylor taylored a polynomial fabric that overwhelms the imagination. What is the meaning of an "nth derivative," for example? The graphs help you begin to see what's going on! Taylor Polynomials aren't just "sew sew." They are awe-inspiring! May the nth derivative be with you!
Having the exams next week and was trying 2 understand what the fuck I was looking at, thanks alot for helping me save alot of time, so much better than my teacher!
What I really think is mind-blowing is how you can write so clearly with a mouse. People can't even tell what I'm drawing on Draw My Thing, and I bet if you played that, you'd be drawing the Mona Lisa left and right.
thank you so much...i just watched every series video and it makes perfect sense now. my ap calc test is this Wednesday and i was flipping out cause everytime i took a practice free response i just completely skipped the series question and was getting no points for it, not to mention the multiple choice. thses videos are great and e^(ipi) + 1 = o ...wtf?!
Sorry, I don't I'm going to the university of south florida. Took my exam today, didn't feel so good as compared to my physics exam which i took earlier. We have the hardest tests of all the other teachers in my class for CALCULUS II and I think I've gotten a C or low B on the test. Okay b/c I got A's on my previous Exams! :D
What Sal does at 9:04 is one of the things that make it so easy to learn from him. He clarifies why he is using sin(1) even though it would be obvious to a lot of people. Teachers generally assume that the students know the reasoning behind every single step in their calculations, which isn't always the case.
Thanks a lot, Sal.
9:04
Nice math lesson, but the most important lesson we all learned is to always drink water with your walnuts.
Math is really hard when you trippin on walnuts.
"Sorry I just had some walnuts" lol
"I hope this video gave you some intuition on the Taylor Series. If it didn't, please ignore this video" HAHAHAHAHAHAH BEST ENDING EVER
I was your 100th like! 🥳😁
"Sorry my brain is... I ate too many walnuts" -khan academy tutor
That's actually Sal Khan
I want all my uni fees to go straight to you because you're teaching me more than any of my lecturer's ever could dream of
go bless you idk why I'm paying so much money for uni when I just end up coming here
where do you have to pay for uni? FeelsGoodMan
So you could have a bachelor degree certificate to apply to some shitty job with it, duh
Cuz u need a motive for coming here to exhaust ur brain
US and Canada for sure
@@Glendragon almost everywher except for norway maybe
I seriously can't thank you enough. My math professor's ineptitude is rivaled only by your competence in explaining the same material. I went into that lecture less confused than I was leaving, whereas this video provides a crystal-clear explanation. Who knows? If there were someone like you for every major subject, TH-cam could serve as a viable replacement for college. Cheers!
o/
Reading the comments before watching the video was really confusing hahaha
Note to self: do not eat walnuts before exams.
Adding more terms makes the approximation of the function better at all points (not just at C). Even with just the first term, P(c)=f(c).
i pay you nothing yet you teach me a lot. i spend all my parents saving to my university and i get nothing.
in 18 minutes you taught me a whole chapter of my maths book that my lecturer couldn't teach me in a 2 hour lecture.
thanks sal!
I had the assigned notes on this for my calculus course, but I couldn't understand. I read it over, and over, and gave a week space in between so I can have a fresh look at the concept of Taylors Polynomial. I heard your site, checked out on how you were teaching the concept... and wow... best 18 minutes of my life spent ACADEMICALLY! Thank you.
Don't be sorry Sal, you deserve all the walnuts you could ever want for explaining this so well! I wish more people would take the time to explain the reasons behind maths functions, it makes it so much easier to see why and what's happening.
I did the former. Each added term contributes to the approximation and doesn't replace it. So the approximation with 100 terms would be much better than the approximation with 2 terms.
The next time I'm not studying for a calculus exam, I'm going to try and computer formulas eating walnuts. Sal, you're the best!
this is truly amazing, with limited class time there is no way anyone can understand this shit. Thank you Khan Academy, for all the review.
Had Numerical Analysis class for the first time at the start of semester today. He made me feel like a complete moron because he sped through Taylor Polynomials in class as if it was the simplest thing in the world to just pick up. This taught me more in 18 minutes than my teacher could in an hour and fifteen.
Seriously, why can't more professors be this good?
oh my. Khan Academy's videos are something that i never regret watching!
Best 18 minutes spent
"My brain had too many walnuts" lololol xD
this. is. amazing. I completely understand how taylor polynomials work now. Taylor was a genius.
amazing. i sat through an entire hour of this and learned literally nothing. then i watch this video and i understand perfectly. thank you kind sir
This is just fantastic! At my university I was only taught how to use the Taylor Series like it's some magical formula you just have to remember, but don't need to understand. In less than twenty minutes you managed to explain what exactly it is and how it is used. Thanks a lot!
To answer a question that's popped up a couple times below: Doing a Taylor expansion for certain functions makes evaluating them around a certain point easier than evaluating the actual function. For example, doing this for sin(x) or tan(x) for SMALL values of x, the later terms of the expansion are so small that you can approximate sin(x) [or tan(x)] to equal x. Cool, right?
Here's what I mean: en.wikipedia.org/wiki/Small-angle_approximation
khan saved my linear algebra and now my calculus too. thanks alot haha
I can understand the effect of walnuts
this is amazing since, after seeing so many classes, and knowing that males are visual, only this guy decides to make taylor visual. Thx for putting "visual males" and "math" together.
8 words:
thanks very much for this video.
sweet explanation.
My exam is in 2 and a half hours and i only just learned taylors method from this video. thanks man.
I reviewed these videos again, and understand it now. Indeed, even the approximation at n=0, that is, where it's just a straight line or constant, is equal to the function at point c. Making the approximations better by adding more terms gives you better approximations at points "near" c and, with even better approximations with more terms, further away from point c. THANKS SAL!
NOW thats the intuition behind the taylor! thx
2nd video ive seen where hes choking on walnuts
Khan should get a Nobel Peace Prize for giving people around the globe access to education for free
Holy shit O.O
I've not gone to a single lesson we have so far because the teacher is so bad, and i think i'm about to pass the whole course just by your videos.
Now you just taught me in 18 mins, what my Maths professor wasn´t able to teach me in like 3 lectures of 90 mins each! Thanks!
nice work you have changed my attitude to the tailors theorem
How the fuck do people just come up with this stuff? its amazing
With walnuts
Jesus
i love you.
you are the reason a never ever have to go to math lectures/tutorials :D
@someonetoogoodforyou
The nth derivative is not equal to the function. It's equal to the function at c. As the nth derivative approaches infinity, not only does p(x) equal f(x) at c, but some of the terms near c of p(x) are close to the terms of f(x) near c. The more derivatives, the closer the values near c of p(x) are to the values near c of f(x) and the farther from c you can approximate. Theoretically, taking infinite derivatives will make the two functions equal for all x.
This was the most beautiful thing I've ever seen in math
Once you GET the Taylor Polynomials...it really does blow the mind into orbit for a while.
i see a bit of remainder therorem here...where polynomials is evaluated at c and its easy to understand only if you know FIRST PRINCIPLE OF DIFFERENTIAL AND TRIGONOMETRY WELL. THE reason I say first principle is you need to know why derivative of sin cos tan cosec sec and all...
You have no IDEA how truthful that statement is.
Thank you so much man! I didn't understand this concept well during class and this really cleared up Taylor Polynomial's for me!
Oh that's just great..now after weeks...countless hours...and lim (brainpain --> oo), I find this.
Great work!
wow thank you so much, my ap exam is in 3 days and i had NO idea how to do series before, just skipped all of the questions.
I Really Like The Video From Your Approximating a function with a Taylor Polynomial
look for the video entitled Euler's Formula and Euler's Identity IT WILL BLOW YOUR MIND!!
this 18 minutes teached me more than the 2 hours i wasted today in the school lyrbrary
Really Great lesson! So good! I recommend it to anyone trying to understand Taylor polynomials. Khan academy is amazing
This has been incredibly helpful-along with many of your other videos.
Just wanted to say, I bet the reason everybody is on this video is because their professors make it SO difficult to understand.
This makes it look SO easy so thanks again Sal =)
You make so much more sense than my Bus Cal 2 prof
@makmegs Don't be selfish. Your not the only one that needs his help.
I only learned how old this video really was when he started to plot the graphs😂. Wait, desmos in the 00s!?
I LOVE YOU KHAN ACADEMY
I like your funny words, magic man.
Nicely stitched video. Taylor taylored a polynomial fabric that overwhelms the imagination. What is the meaning of an "nth derivative," for example? The graphs help you begin to see what's going on! Taylor Polynomials aren't just "sew sew." They are awe-inspiring! May the nth derivative be with you!
Thanks, straightened the Taylor polynomial out for me in 20 mins... should have looked this one up sooner :)
Aww thank you :) Exam tomorrow... This really helped XD
yes it is the same level. maclaurin is just the special case where your center, a, is defined at 0, a = 0.
Sir , i can't express my gratitude to you in words
You help me a lot
Basic but well done! I have to relearn multi variable taylor now..
You are blowing dust out of my 👂 , thank you
You makes my studies 10 times easier. 💯👍👍
amazing video, even in 2021
thanks for this fun explanation!, a student from the future
Having the exams next week and was trying 2 understand what the fuck I was looking at, thanks alot for helping me save alot of time, so much better than my teacher!
4:44 - 6:28 Best two minutes of this vid for me :D
What I really think is mind-blowing is how you can write so clearly with a mouse. People can't even tell what I'm drawing on Draw My Thing, and I bet if you played that, you'd be drawing the Mona Lisa left and right.
i learn more from khan than all my math teachers combined
My school actually sent an email to everyone to watch your videos to prepare for our finals!
Why can't my maths lecturer explain things this well. He takes 10 times as long to teach us absolutely nothing.
you save my life consistently
thank you so much...i just watched every series video and it makes perfect sense now. my ap calc test is this Wednesday and i was flipping out cause everytime i took a practice free response i just completely skipped the series question and was getting no points for it, not to mention the multiple choice. thses videos are great and e^(ipi) + 1 = o ...wtf?!
Walnuts: The Kryptonite to all mathematicians.
omg math is so beautiful ... and extremely well explained, thanks a lot !!
wow.....now i get it....thank you Master
"my brain is a bit urgh, i ate to many walnuts"
Educational AND amusing..
Win! ^.^
this video is crucial!
Thank you very much! I read the book but could not understand until I watched this video!
lmao @ 'if it didnt ignore this vid...' srly who wouldnt understand after that comprehensive session... thanks heaps sal... thanks...
Thank you SO MUCH
This Got cleared !!
tanx for the lecture mr. khan, i like your teachin alot....
its helps me more than my boring ass lecturer
Tank you very much sir, very simple and intuitive explanation
Taylor series is so beautiful . I literally have tears in my eyes
wow that's... a deep understanding of it
final calc exam tomorrow, never learned this stuff... combination of you + my book = win :>
love your videos!!! thank you very much!!! Knowledge is for humans!!! :D... greetings from mexico
"I ate too many walnuts..." - Classic!
Thanks for the help sal!
Fantastic video
Thanks for this.
Sorry, I don't I'm going to the university of south florida. Took my exam today, didn't feel so good as compared to my physics exam which i took earlier. We have the hardest tests of all the other teachers in my class for CALCULUS II and I think I've gotten a C or low B on the test. Okay b/c I got A's on my previous Exams! :D
great, better than the teachers.
great lesson
thanks for the video. I like how you apply the equation directly into a graph, thanks
Holy cow! This makes so much sense now. Thank you.
Nice explained
you're amazing!!!!! loved the calculation part at the end
you can do that. but only if it is centered at 0. if it is, half of your terms drop out